Summary Managerial Statistics - When To Use Which Test

Managerial Statistics
(9th edition – Gerald Keller)



When To Use Which
Test (Statistics)
OVERVIEW OF ALL STATISTICAL TEST AND THEIR PURPOSE
(INCLUDING PAGE NUMBERS)




University of Groningen

,Interval  Temperature, the intervals between each value are equally split
Nominal  Categorical, passed" vs. "failed" by "male" vs. "female"
Ordinal  Rating scale from 1 to 5
Ration  Time, data is interval data with a natural zero point

Describe population
Ordinal data is not statistically covered

NOTE! Standard deviation is the square root of the variance

Interval data
Z-test to calculate specific area (known deviation) (267): Calculate the probability that a
specific value falls into a specific interval (i.e. calculate when to repair/reorder something).
Calculate reorder point (p.278).
 Calculate left area: P(X<Y)  P(Z<Y)
 Calculate right area: P(X>Y)  P(Z>Y) = 1 – P(Z<Y)
 Calculate area between two points: P(Z<Y) – P(Z<Y) (right boundary minus left
boundary)
 When sample size is known, use formula on P.312


Z-test to calculate population mean (known deviation) (confidence interval, 334):
Calculate population mean when the population standard deviation is known and the
population is normally distributed.
Confidence levels and their Z-values
 A = 0.1 A/2 = 0.05 Z0.05 = 1.645
 A = 0.05 A/2=0.025 Z0.025= 1.96
 A= 0.02 A/2= 0.01 Z0.01= 2.33
 A= 0.01 A/2= 0.005 Z0.005 = 2.575
 Calculate sample size (P.348)


T-test to calculate specific area (unknown deviation) (394): Test a hypothesis about the
population mean (area smaller or larger than the mean) by using a sample, when the
when the population standard deviation is unknown and the population is normally
distributed.
Degrees of freedom: V= n – 1
 Calculate left area (<): rejection region T < a/2, v-1 < – (critical value)
 Calculate right area (>): rejection region T > a/2, v-1 + (critical value)
 Calculate right area (≠): rejection region T ≠ a, v-1 +– (critical value)

, T test to calculate population mean (unknown deviation) (confidence interval, 394):
Calculate population mean by using a sample when the population standard deviation is
unknown and the population is normally distributed. (One sample T-test, no relationship
between the observations)
Degrees of freedom: V= n – 1
 Use formulas on page 398


X²-Test (Chi-Squared) and estimator of population variance (408): Used to determine the
variance of a population based on a sample. Estimate variance interval (P. 408)
Degrees of freedom: V= n – 1
 Calculate left area (<): rejection region, X² < X² 1-a, n-1
 Calculate right area (>): rejection region, X² > X²a, n-1
 Calculate left and right area (≠) rejection region, X² ≠ X²a/2, n-1

Nominal data
Two categories
Z-test and estimator of P (population proportion) (confidence interval, 417,421): Used to
calculate how a sample is distributed (proportion of successes). (When P-hat, X/n, is
unknown, use 0.5).
Z-test and estimator of P (population proportion) (test hypothesis, 418): Used to test
statements about the amount of successes within a population.
 Calculate left area: P(X<Y)  P(Z<Y)
 Calculate right area: P(X>Y)  (P(Z>Y) = 1 – P(Z<Y)
 Calculate area between two points: P(Z<Y) – P(Z<Y) (right boundary minus left
boundary)
Rejection region: Za


 P. 320 for P-hat (without Z-score, same formula though)
 P. 422: select sample size needed to estimate the proportion


≥ Two categories (groups) – independent observations - variable must be mutually
exclusive (only A or B, not both can occur) - at least 5 expected frequencies in each group
of the variable
X²- goodness-of-fit test (578, 579): calculate how "close" the observed values are to those
which are expected. Does it fit the expectance? A small test statistic supports the null
hypothesis.
Rejection region: X² > X² a, k-1 (where k is the number of variables i.e. cells).
 Fi: observed frequency
 Ei: Expected frequency